We propose a simple approach to address these cases. 1) Build a generous effective state space \(\Omega _B\)  by assigning different reduced states to every two states in \(\Omega \)  that can be distinguished in principle by the agent. 2) Build an approximation structures in the effective state space [1]}. An approximation structure comprehends all neighbourhoods \(\lbrace  \mathcal {B}^\varepsilon (\rho )\rbrace _{\rho \in \Omega _B, \varepsilon \in \mathcal {E}}\)  parameterized by whatever measure \(\mathcal {E}\)  is operational for the agent. For example, one valid approximation structure for quantum states corresponds to the \(\varepsilon \) -balls induced by the trace distance; another could be just the cover \(\lbrace \) blue, green, ...\(\rbrace \)  of the possible colours assigned to each frequency. 3) Build notions of approximate secrecy, where we can demand for example
\( B \circ f_B \circ g_A (\rho )\ \in \mathcal {B}^\varepsilon (B \circ f_B (\rho )),\) 
